It's well worth a read if you're interested in an interesting and somewhat provocative take on the Star Wars films. But what drew my attention was the description of the Lord of the Rings as a "reactionary fantasy", which left me wondering how true that was.
Certainly Tolkien himself was an instinctive conservative, to the point that when the Catholic Church switched the liturgy from Latin to English, he carried on reciting it in Latin regardless. Though, interestingly, Tolkien characterised his own political views as a combination of anarchism and monarchism. As far as I can see that means a King with ultimate political power who is wise enough not try and use it to actually do anything. This attitude is certainly reflected in Tolkien treatment of the Shire, in many ways Tolkien preferred idea of society. The hobbits elect a mayor, but his principle role is to preside over banquets, while the closest thing the hobbits have to a police force, the shirrifs, are mostly interested in wondering about gathering news and gossip. When the someone tries to actively change things in the Shire, it all goes horribly wrong.
In many ways this is the instinctive conservatism of the comfortably off, thinking that the world is just fine the way it is and everything would be okay if everyone was just left alone. This allows you to ignore the fundamental injustices and inequalities in the world and insist that everyone would be better off if they understood their place.
However, despite Tolkien's overt political views, there is an undercurrent in the Lord of the Rings that works against this. The principle goal of the characters in LOTR is the destruction of the One Ring, but the overall theme is of the last days of a heroic and magical age. Along with the destruction of the Ring and the Dark Lord Sauron, the more magical races, the elves, the dwarves and even the hobbits will go into decline, with humans becoming ascendant, the Wizards will also depart and the more magical and fantastic elements of the world pass away. This dichotomy is most firmly stated by Galadriel
"Do you not see now wherefore your coming is to us as the footstep of Doom? For if you fail, then we are laid bare to the Enemy. Yet if you succeed, then our power is diminished, and Lothlorien will fade, and the tides of time will sweep it away. We must depart into the West, or dwindle to a rustic folk of dell and cave, slowly to forget and to be forgotten."
The Lord of the Rings, Book 2, Chapter 7, The Mirror of GaladrielIn spite of this, there is never any question that the destruction of the Ring is anything other than a good and necessary thing. Discussions of trying to hide the ring are quickly glossed over and its emphasised again and again that the ring cannot be used for good. When the ring is finally destroyed the tone is entirely celebratory.
"This is the ending. Now not day only shall be beloved, but night too shall be beautiful and blessed and all its fears pass away!"
Frodo, The Lord of the Rings, Book 6, Chapter 5, The Steward and the KingSo the passing of the old magical world into a new more mundane but safer one is regarded as a good thing, despite the loss of the positive aspects of the old.
Tolkien's attitude to the hobbits is similarly ambivalent. The hobbits are treated as peaceful and harmless but, with a few notable exceptions, parochial, prejudiced and xenophobic. A humorous touch in the first book of LOTR has the inhabitants of Hobbiton repeatedly describing the people of Buckland, on the other side of the Shire as "queer folk", but as soon as Frodo and his friends reach Buckland they hear the Bucklanders using the same term to describe the people of Hobbiton. Frodo himself sums up this contradiction.
"I should like to save the Shire, if I could - though there have been times when I thought the inhabitants too stupid and dull for words, and have felt that an earthquake or an invasion of dragons might be good for them. But I don't feel like that now. I feel as long as the Shire lies behind, safe and comfortable, I shall find wandering more bearable: I shall know that somewhere there is a firm foothold, even if my feet cannot stand there again."
The Lord of the Rings, Book 1, Chapter 2, The Shadow of the Past
In spite of this, Frodo ultimately fails. He is not able to stop the War of the Ring touching the Shire and returns to find it ruined. And yet, the hobbits rally round, defeat their enemies and become a broader minded people as a result, albeit in a small way. If you read the Appendices to LOTR, it is revealed that following the events in the main story, the hobbits expanded the Shire, settling to the west and that the King ultimately visited, setting up his court to the east of the Shire for over a year. If the hobbits didn't exactly embrace the outside world, they at least grudgingly accepted its existence.
Tolkien disliked the the term allegory, preferring the term applicability. But if we apply the ideas of the Lord of the Rings to the real world, what does it say? That, ultimately, we have to deal with problems and can't just ignore them and that we cannot defend the status quo regardless of the consequences. That change will occur, but that this is not inherently negative. I'm not sure this can be regarded as a reactionary message.